Stochastic persistence and stationary distribution in a Holling-Tanner type prey-predator model

► A predator-prey model with Beddington-DeAngelis functional response is considered. ► Stochastic dynamics is analyzed to study the effect of fluctuating environment. ► We proved the existence and uniqueness of global solution for SDE model. ► Strong persistence and stationary distribution for both populations are established. ► Exhaustive numerical simulations are carried out to validate the analytical findings.